Homogenization of the Robin problem for the Poisson equation in a thick multi‐structure of type 3:2:2

Article type: Research Article

Authors: De Maio, U. | Mel'nyk, T.A.^;

Affiliations: Dipartimento di Matematica e Applicazioni, Università degli Studi di Napoli Federico II, Complesso Monte S. Angelo – Edificio “T”, Via Cintia, 80126 Napoli, Italia E‐mail: udemaio@unina.it | Faculty of Mathematics & Mechanics, Taras Shevchenko University of Kyiv, Volodymyrska str. 64, 01033 Kyiv, Ukraine E‐mail: melnyk@imath.kiev.ua

Note: [] Corresponding author.

Abstract: In this paper we study a mixed boundary value problem for the Poisson equation in a multi‐structure Ωε, which is the union of a domain Ω0 and a large number N of ε‐periodically situated thin rings with variable thickness of order ε=𝒪(N−1). By using some special extension operator, we prove a convergence theorem as ε→0 and investigate the asymptotic behaviour of the solution under the Robin conditions on the boundaries of the thin rings.

Keywords: homogenization, extension operator, thick multi‐structure

Journal: Asymptotic Analysis, vol. 41, no. 2, pp. 161-177, 2005